2 mcqs

(8) Induced emf ε = - N Δϕ/Δt . The rate of change of the flux with time is increasing all of the time so this rules out answer D as D's graph says that ε stays constant. It also rules out answer C as C shows that ε is decreasing. Now, at time t=0, the graph of flux against time is showing the line going upwards i.e. the rate of change of flux is a positive, non zero number. So, this rules out A because for the emf to be zero, the graph of flux against time would have to be flat at t=0. This therefore leaves B as the correct answer.


(7) Charge is conserved as there are two positive charges on each side of the equation, so it's not A.
There isn't a conservation of particle numbers rule so it's not B
There would only be a very high value for kinetic energy for the resultant particles if the total energy before was much greater than the sum of the rest masses after, so it's not D. (rest energy of a proton = 938.28MeV, rest energy of a neutron = 939.57MeV, rest energy of the pion = 139.57MeV.)
This leaves C. There needs to be a certain minimum kinetic energy in order to have the interaction between the two protons and for them to produce the resultant particles as the total of the energies on the right hand side is more than the total on the left hand side of the equation.

(8) The flux is zero at t=0 but the rate of change of flux is not zero, it is positive and non zero. It is the rate of change of flux that determines the emf.
(7) The total energy on each side of the equation must be the same (conservation of energy). The total of the rest energies on the left added to any kinetic energy on the left must equal the total of the rest energies on the right added to any kinetic energy the resultant particles may have. Since the rest energies on the right is higher than that on the left, the kinetic energy on the left hand side would have to be at least enough to produce all of the "extra" rest energy on the right. (Add the rest energies together for each side to see what I mean.) However, there is no requirement for the particles on the right to have any kinetic energy in order for the reaction to occur. In other words, any kinetic energy on the right is only there if there is "extra" energy left over from producing the particles.